Abstract

A maximal-acceleration invariant quantum field is defined on the
space-time tangent bundle with vanishing eigenvalue when acted on
by the Laplace-Beltrami operator of the bundle, and the case is
addressed in which the space-time is Minkowskian, and
the field is Lorentz invariant. In this case, the field is shown
to be automatically regularized at the Planck scale, and particle
spectra are cut off at extremely high energies. The microcausality
is addressed by calculating the appropriate field commutators;
and it is shown that provided the adjoint field is consistently
generalized, the necessary commutators are vanishing and the
field is microcausal, but that there are Planck-scale
modifications of the boundary of the causal domain that are
significant for extremely large relative four-velocities between
the separated space-time points. For vanishing relative
four-velocity, the causal domain is canonical. The geometry of the
causal domain indicates that near the Planck scale, causal
connectivity may occur between spacelike separated points, and
also at larger scales for extremely large relative
four-velocities.

Copyright Hindawi Publishing Corporation. The ELibM mirror is published by FIZ Karlsruhe.